Subject GRE-Style: Taylor Series Application

GRE Math Subject · Axiom Academy

EXAMPLE GRE-Style Taylor Series Application We need the Taylor expansions of e^x and : Replace x with x^2 in the e^x series: To find the coefficient of x^3 in , we multiply: To get x^3 terms, we need products that give x^3 . However, since e^ x^2 only contains even powers and has only even powers, their product only contains even powers! Since e^ x^2 is an even function (only even powers of x ) and is also an even function, their product is even. Therefore, there are no odd-powered terms in the expansion. GRE Insight: Before doing tedious computations, check symmetry properties. Even×even = even, odd×odd = even, even×odd = odd. This saves enormous time!

This is the written version of the interactive lesson above. See the full GRE Math Subject course.